Ivan, Bobby and Ryan shared a bag of buttons. Bobby took 37 as many buttons as Ryan. Ivan took twice as many buttons as the total Bobby and Ryan took. After Ivan had given 24 to Bobby and 6 to Ryan, Bobby gave 3 to Ryan. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Ivan and Bobby had at first.
| |
Bobby |
Ryan |
Ivan |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 24 |
|
- 24 |
|
| Change 2 |
|
+ 6 |
- 6 |
|
| Change 3 |
- 3 |
+ 3 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of buttons that Bobby and Ryan had at first
= 3 u + 7 u
= 10 u
Number of buttons that Ivan had at first
= 2 x 10 u
= 20 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 30 is 30.
Number of buttons that Ryan received from Bobby and Ivan
= 10 u - 7 u
= 3 u
3 u = 6 + 3
3 u = 9
1 u = 9 ÷ 3 = 3
Difference between the number buttons that Ivan and Bobby had at first
= 20 u - 3 u
= 17 u
= 17 x 3
= 51
Answer(s): 51
